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# For how many integer values of x

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Intern
Joined: 20 May 2019
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For how many integer values of x [#permalink]  08 Jun 2019, 05:50
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Question Stats:

100% (00:01) correct 0% (00:00) wrong based on 1 sessions
For how many integer values of x, is |2x−5|+|x+1|+|x|<10?

A. 1
B. 2
C. 4
D. 5
E. Infinite
[Reveal] Spoiler: OA
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Re: For how many integer values of x [#permalink]  09 Jun 2019, 10:17
Expert's post
Taking all positive terms :

$$2x-5+x+1+x<10$$

$$4x-4<10$$

$$x<\frac{7}{2}$$

Taking all negative terms :

$$5-2x-x-x-x<10$$

$$x>-\frac{3}{2}$$

So the range is $$-\frac{3}{2}<x<\frac{7}{2}$$

Therefore , the possible values are -1,0,1,2,3...so 5 values
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Re: For how many integer values of x   [#permalink] 09 Jun 2019, 10:17
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